The composite optical vortices (OVs) formed by two parallel, off-axis Hermite-Gaussian (H-G) vortex beams at the waist plane and their evolution behavior are studied. It is shown that the number, position and net topological charge of composite OVs depend not only on the control parameter, including the relative phase, amplitude ratio, waist width ratio and off-axis distance, but also on the mode structure of H-G vortex beams. By appropriately varying the control parameter and mode of H-G vortex beams and in the free-space evolution, the motion, creation and annihilation of composite vortices may appear, and the topological charge does not always remain unchanged. In particular, for the composite OVs formed by TEM00 and TEM01 vortex beams, the topological charge is not conserved by changing relative phase. The results are useful for the composite OV control and applications.